fulltext

DOI 10.1393/ncc/i2005-10038-0

IL NUOVO CIMENTO Vol. 28 C, N. 3 Maggio-Giugno 2005

Autocorrelation analysis of GRBM–Beppo-SAX burst data(∗)

(1) Stockholm Observatory, AlbaNova - SE-106 91, Stockholm, Sweden (2) Dipartimento di Fisica, Universit`a di Ferrara - 44100 Ferrara, Italy

(3) Istituto di Astrofisica Spaziale e Fisica Cosmica, CNR - 90146, Palermo, Italy (ricevuto il 23 Maggio 2005; pubblicato online il 16 Settembre 2005)

Summary. — An autocorrelation function (ACF) analysis was performed on 17

gamma-ray bursts with known redshift, using data from the GRBM on board Beppo-SAX. When corrected from the cosmic time dilation effect, the ACFs show a bimodal distribution at about half-maximum, in agreement with a previous study based on BATSE and Konus burst data. Although the results show more dispersion, the separation between the two classes is highly significant.

PACS98.70.Rz – γ-ray sources; γ-ray bursts. PACS01.30.Cc – Conference proceedings.

1. – Introduction

The study of time scales is essential for the physical understanding of any astronomical phenomena. For gamma-ray bursts (GRBs) though, no characteristic time has been clearly identified, aside from the time duration of the events in the observed energy band. Individual power density spectra (PDS) are in general very diverse, but the average PDS of many bursts showed a power-law behaviour over two frequency decades, suggesting the absence of any preferred time scale [1]. However, since long bursts are at cosmological distances, it is likely that some temporal features might be blurred by time dilation effects. In a recent analysis of 16 long GRBs with known redshiftz, that were detected by the BATSE and Konus experiments, it was shown that when corrected for cosmic time dilation the autocorrelation function (ACF) exhibits a clear bimodal distribution [2]. Taking as a measure the half-width at half-maximum, there is a highly significant gap between a narrow and a broad width class, the separation in standard deviations being > 7σ. The average widths (relative dispersions) are 1.6 s (32%) and 7.5 s (4%) for the narrow and broad classes, respectively. The results in [2] were based on a small number of observations, and therefore need to be confirmed by a larger statistical sample. In this paper we present preliminary results of an extension of that work using GRB data from

(∗) Paper presented at the “4th Workshop on Gamma-Ray Burst in the Afterglow Era”, Rome, October18-22, 2004.

c

276 L. BORGONOVO, F. FRONTERA, C. GUIDORZI, ETC. -15 -10 -5 0 5 10 15 20 0 0.2 0.4 0.6 0.8 1 ACF -15 -10 -5 0 5 10 15 20 τ [s] 0 0.2 0.4 0.6 0.8 1 ACF a) b)

Fig. 1. – a) Observed autocorrelation functions of 17 GRBM bursts. b) Local ACFs where the time dilation effect has been corrected, withτ
=τ/(1 + z). Although not as clearly as with BATSE data, two width classes are noticeable at half-maximum. The gap separation represents a 3.1σ deviation with a chance probability p < 0.0008.

the Gamma Ray Burst Monitor (GRBM) on the Beppo-SAX satellite. The drawback of mixing data from different instruments is that this in itself might introduce more dispersion, that could in fact outweigh the benefits of an increased sample. For this reason we will consider separately the GRBM burst sample and evaluate its suitability for our ACF analysis.

2. – Data and methods

The ACF width shows a dependency with the energy band [3] and, like the pulse structure, it broadens at lower energies. We use the lower energy channel data of the GRBM that, being in the 40–700 keV energy range, roughly matches the BATSE (50– 320 keV) and Konus (50–200 keV) ranges of the previous ACF study [2]. Note that since the ACF is a quadratic function of the number of counts, and there are more counts at lower energies, it is more important the agreement between the lower-end energy limits. The standard high resolution 7.8125 ms data was binned up into a time resolution of 62.5 ms to improve the signal-to-noise ratio (S/N). This has no significant consequence for the measurement of the time scales that concerned us here, and reduces some noise artifacts in the ACF. In addition, it better matches the standard BATSE 64 ms temporal resolution for later comparison. In one case (GRB990510), because the on-board logic was not triggered by the burst, only 1 s data are available. A total of 17 GRBs were included in our sample. The light curves were corrected for dead-time and background subtracted.

To derive the ACF from the GRB light curves we followed the methods described in [2]. From a uniformly sampled count history with ∆T time resolution and N time bins, let mi be the total observed counts at bini. Also let bi be the corresponding background

level andc_i =m_i− b_i the net counts. The discrete ACF as a function of the time lag τ = k∆T is (1) A(τ) = N−1
i=0 cici+k A0 , k = 1, . . . , N − 1

AUTOCORRELATION ANALYSIS OF GRBM–BEPPO-SAX BURST DATA 277

Table_{I. – Sample of 17 GRBs detected by GRBM with known redshift. The first six columns}

give the burst name, the measured redshiftz and the corresponding reference, the width class

(n: narrow, b: broad), the ACFhalf-width at half-maximum τ0, and the corresponding width

corrected for time dilation τ₀
= τ0/(1 + z). The last two columns give, when available for

comparison, the width estimation done based on BATSE dataτ₀B [2], and the relative difference

∆τ₀/ ¯τ₀ with respect to the average value ¯τ₀.

GRB z Ref. Class τ₀(s) τ₀
(s) τ₀B(s) ∆τ₀/ ¯τ₀(%) 970228 0.695 [4] n 1.20 0.71 970508 0.835 [5] n 3.92 2.14 2.70 37.1 971214 3.418 [6] n 8.65 1.96 8.02 8.4 980326 1.2 [7] n 2.44 1.11 980329 3± 1 [8] n 6.14 1.53 5.96 3.0 980425 0.0085 [9] b 8.88 8.81 7.62 15.2 990123 1.6 [10] b 17.43 6.70 19.81 −12.8 990506 1.3066 [11] n 3.51 1.52 3.83 −8.6 990510 1.619 [12] n 3.28 1.25 2.54 25.5 990705 0.86 [13] b 14.28 7.67 990712 0.434 [14] n 4.08 2.84 991216 1.02 [15] n 3.33 1.65 3.80 −13.2 000210 0.846 [16] n 1.91 1.04 000214 0.47 [17] n 2.53 1.72 010222 1.477 [18] n 5.42 2.19 010921 0.45 [19] b 9.81 6.77 011121 0.362 [20] b 10.91 8.01

The normalisation constantA₀ is defined as

(2) A₀=

N−1
i=0

(c2_i − m_i).

The normalisation makes the ACF of each burst fluence independent. The term m_i in eq. (2) subtracts the contribution of the uncorrelated noise assuming that it follows Poisson statistics.

3. – Results and discussion

In fig. 1a we show the observed ACFs of all our GRB sample, and in fig. 1b the local ACFs where the cosmic time dilation effect has been removed, withτ =τ/(1 + z) being the corrected time lag. Though not as evident as when using BATSE data, still two classes given by the local width at half-maximum can be recognised. We focus on the central part of the ACF. In some bursts where the light curve presents a few well separated pulses of similar intensity the ACF shows strong secondary features, while in most cases these secondary peaks are negligible. Our measurements are summarised in table I. Note that although GRB980329 redshift is only known to be in thez = 2.0–3.9 range [8], in any case its ACF would lie within the other narrow width bursts. In fig. 1b we used an average value ofz = 3.

We obtained a mean value of τ(n)₀ = (1.6 ± 0.2) s and τ(b)₀ = (7.6 ± 0.5) s, and a sample standard deviation of σ(n) = 0.7 s and σ(b) = 1.2 s for the narrow and broad

278 L. BORGONOVO, F. FRONTERA, C. GUIDORZI, ETC.

sets, respectively. The gap separation between the two sets represents a 3.1σ deviation. The probability p of a random occurrence of such a gap was estimated using a Monte Carlo simulation, assuming that there are no characteristic time scales. Iwas found that p < 0.0008. The results are fully consistent with [2], as expected if width errors are larger but stochastic, since only 6 GRBs in this paper were not considered before. The main observed difference is the larger dispersion of the second class (∼ 16%), while the first has about the same spread (∼ 43%).

Table Ishows in its last two columns a comparison of the ACFs widths of bursts detected by both GRBM and BATSE. The widths are not systematically broader in the first case (positive differences), therefore the discrepancies can not only be attributed to the different energy range. A better S/N and a more uniform directional response in the BATSE case, our reference instrument, might also be significant factors. The average percentile width difference at half-maximum is ∼ 15%. Therefore the dispersion incre-ment in each class width can be explained taken into account the qualitative difference of the GRBM data.

4. – Conclusions

In this comparative study we found that the ACFs and their derived measurements based on GRBM data are consistent with the previous analysis using BATSE/Konus data. The observed dispersion is larger, but mean values of the characteristic time scales for each width class are equal to within the estimated uncertainties. Consequently, at least for this analysis, we can assume that the errors introduced by the instrument were mainly stochastic. Furthermore, despite the increased spread we were still able to identify two separated classes with a very high confidence level (p < 0.0008).

∗ ∗ ∗

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